Tube or Elizabeth line

Go to TfL.gov.uk and use the Journey Planner. Pay by contactless card or phone. I think you are confusing the Heathrow Express and the Elizabeth Line.

The Piccadilly line will cost about 6£. The previously mentioned website will provide an exact amount. For Shepherd’s Bush it may be easier to take the Elizabeth Line to Ealing Broadway then switch to the Central Line.

There are multiple stations called Shepherds Bush. If you tell us where in Shepherds Bush you are going, we can better help.

The Piccadilly line doesn't go to any of them and you will have to change. The same is true for the Elizabeth Line. However, if you stick to the tube, ti will be cheaper.

As of now, from Heathrow to either of the Shepherd Bush stations, the fare is 2.10 GBP. It is going up slightly next month

BTW, discounted tickets are for the Heathrow Express and not the Elizabeth line.

If you are going to the station called Shepherd's Bush, the easiest/fastest way is what has been mentioned here- Elizabeth line to Ealing Broadway and Central line to Shepherd's Bush. This will cost £7.10 off peak. If you are going to Shepherd's Bush Market, easier to take the Piccadilly line to Hammersmith and change to Hammersmith and City/Circle- tho that change involves getting out of one station, crossing a street and entering another station, which is a bit of a pain with luggage. That will be £2.10 off peak. You can't book any of these in advance. Sometimes there is engineering work on the weekend so make sure you are checking Google maps or the TFL website for the specific day you want to travel.

Thanks for the great comments.